Nine-parameter path synthesis of planar four-bar mechanism with the aid of the general equation of coupler curve

The design of a four-bar mechanism to generate a prescribed path with minimal error is possible by using the maximum number of parameters that are effective in the path synthesis of the mechanism. In this study, the design of four-bar mechanisms, which intersect the given path curve at nine points, was dealt with in two stages. In the first step, the kinematic equations of the mechanism were used to implement the preliminary design based on the five parameters and closed-form solving. Thus, all the possible solution values have been reached with five parameters. In the second stage, which is the final design, the general algebraic form of coupler curve, which is dependent on the nine dimensions of the mechanism and of the sixth order, was obtained. An objective function de-rived from the obtained equation is subjected to an optimization process with nine-parameters by using the dimensions obtained from the preliminary design as an initial value, and the error between the actual and the desired path is minimized. The efficiency of the method is shown by numerical example made by choosing difficult paths to produce four-bar mechanisms.